A mathematical model is proposed to the pulsatile flow of blood in a tapered artery with mild constriction. This study considers blood as an electrically conducting, non-Newtonian fluid (Jeffrey fluid) which contains magnetic nanoparticles. As blood conducts electricity, it exerts an electric force along the flow direction due to the induced magnetic force by an applied magnetic field which produces

We present a strategy for image data sparsification based on a multiple multiresolution representation obtained through a structured tree of filterbanks, where both the filters and decimation matrices may vary with the decomposition level. As an extension of standard wavelet and wavelet-like approaches, our method also captures directional anisotropic information of the image while maintaining a controlled

Statistical models are often structurally unidentifiable, because different sets of parameters can lead to equal model outcomes. To be useful for prediction and parameter inference from data, stochastic population models need to be identifiable, this meaning that model parameters can be uniquely inferred from a large number of model observations. In particular, precise estimation of feeding rates in

We focus on strongly connected, strong for short, digraphs since in this setting distance is defined for every pair of vertices. Distance ideals generalize the spectrum and Smith normal form of several distance matrices associated with strong digraphs. We introduce the concept of pattern which allow us to characterize the family Γ1 of digraphs with only one trivial distance ideal over Z. This result

Cooperation plays a crucial role in addressing social dilemmas, yet inequality complicates the achievement of cooperation. This paper explores how environmental feedback mechanisms influence the evolution of cooperation within unequal groups. We construct a public goods game model that includes productivity and endowment inequalities and introduce a dynamic environmental feedback mechanism to study

Using the O'Nan-Scott Theorem for classifying the primitive permutation group, the classification problem of 3-design is discussed. And the block-transitive and point-primitive automorphism groups of a 3-(v,k,2) designs is reduced to affine type and almost simple type.

A span of a given graph G is the maximum distance that two players can keep at all times while visiting all vertices (edges) of G and moving according to certain rules, that produces different variants of span. We prove that the vertex and edge span of the same variant can differ by at most 1 and present a graph where the difference is exactly 1. For all variants of vertex span we present a lower bound

An induced matching is defined as a set of edges whose end-vertices induce a subgraph that is 1-regular. Building upon the work of Gupta et al. (2012) [11] and Basavaraju et al. (2016) [1], who determined the maximum number of maximal induced matchings in general and triangle-free graphs respectively, this paper extends their findings to connected graphs with n vertices. We establish a tight upper

The maneuvering problem for nonlinear systems under stochastic disturbances is investigated in this paper. Firstly, the maneuvering control objectives in their stochastic version are described in the sense of moment with tunable design parameters. Then, quartic Lyapunov functions of stabilizing errors are adopted to deal with the unknown covariance noise. Based on the adaptive law and the filter-gradient

This article investigates the containment control problem for multi-agent systems (MASs) that are affected by aperiodic denial-of-service attacks using event-triggered strategies (ETSs) in a directed graph. To overcome the limitation of the Luenberger observer, which requires a trade-off between rise time and overshoot, we design a reset observer with improved error convergence performance and more

We propose a level set method for a Stokes eigenvalue optimization problem. A relaxed approach is employed first to approximate the Stokes eigenvalue problem and transform the original shape optimization problem into a topology optimization model. Then the distributed shape gradient is used in numerical algorithms based on a level set method. Single-grid and efficient two-grid level set algorithms

Fast and accurate predictions of the spatiotemporal distributions of temperature are crucial to the multi-scale thermal management and safe operation of microelectronic devices. To realize it, an efficient semi-implicit Lax-Wendroff kinetic scheme is developed for numerically solving the transient phonon Boltzmann transport equation (BTE) from the ballistic to diffusive regime. The biggest innovation

In order to provide a more effective method to describe the local structure of the degraded image and to enhance the robustness of the denoising, we propose a non-convex total variational image denoising model that combines the non-convex log function with an adaptive weighted matrix within the total variation framework. In the proposed model, the weighted matrix is capable of effectively describing

This study employs an integral transform approach for Love wave propagation in a rotating composite structure having an interfacial crack. The structure comprises an initially stressed functionally graded piezoelectric-viscoelastic half-space bonded to a piezoelectric-viscoelastic half-space, and is subjected to anti-plane mechanical loading and in-plane electrical loading. The study focuses on two

In the face of collective motion, people often face a binary decision: they may interact with others and pay for communication, or they can choose to go alone and forgo these costs. Evolutionary game theory (EGT) emerges in this setting as a crucial paradigm to address this complex issue. In this study, an EGT-based Vicsek with a fixed number of neighbors is proposed. It assumed that the agent had

As the number of links and processors in an interconnection network increases, faulty links and processors are constantly emerging. When a network fails, how to evaluate the state of the network and optimize the reliability of the network itself is the focus of attention in recent years. Therefore, the design of network structure and network reliability evaluation are particularly significant. In recent

The dissemination of information and the adoption of immunization behaviors are vital for preventing infection during epidemics. Positive and negative information have different influences on the decision to accept immunization behaviors, and individuals make decisions about whether to accept immunization based on both subjective cognizance and objective environmental factors. A three-layer propagation

This note considers the computation of the logarithm of symmetric positive definite matrices using the Gauss–Legendre (GL) quadrature. The GL quadrature becomes slow when the condition number of the given matrix is large. In this note, we propose a technique dividing the matrix logarithm into two matrix logarithms, where the condition numbers of the divided logarithm arguments are smaller than that

In this article, a mixed spectral element method combined with second-order time stepping schemes for solving a two-dimensional nonlinear fourth-order fractional diffusion equation is constructed. For formulating an efficient numerical scheme, an auxiliary function is introduced to transform the fourth-order fractional system into a low-order coupled system, then the time direction is discretized by

In finite element methods for incompressible flows, the most popular approach to allow equal-order velocity-pressure pairs are residual-based stabilisations. When using first-order elements, however, the viscous part of the residual cannot be approximated, which often degrades accuracy. For constant viscosity, or by assuming a Lipschitz condition on the viscosity field, we can construct stabilisation

The two-dimensional (2D) Kuramoto-Sivashinsky equation offers a robust framework for studying complex, chaotic, and nonlinear dynamics in various mathematical and physical contexts. Analyzing this model also provides insights into higher-dimensional spatio-temporal chaotic systems that are relevant to many fields. This article aims to solve the scalar form of the two-dimensional Kuramoto-Sivashinsky

This study investigates the application of wetting boundary conditions for modelling flows in complex curved geometries, such as rough fractures. It implements and analyses two common variants of the wetting boundary condition within the three-dimensional (3D) phase field lattice Boltzmann method. It provides a straightforward and novel extension of the geometrical approach to curved three-dimensional

Traditional transform thermodynamic devices are designed from anisotropic materials which are difficult to fabricate. In this paper, we design and simulate a carpet thermal concentrator. Based on existing transformation thermodynamic techniques, we have derived the perfect parameters required for carpet heat concentrators. In order to eliminate the anisotropy of perfect parameters, we designed a heat

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the second-order total variation of each trainable activation. The slope constraints allow us to impose properties such as 1-Lipschitz stability, firm non-expansiveness

We express the interpolating cubic splines of class C2 in their new, explicit forms. We construct the desired forms, the spline's Hermitian and B-spline representations for both equidistant and arbitrary nodes. During this process we demonstrate an innovative way to compute the inverse of a special class of tridiagonal matrices. Afterward, we propose the corresponding interpolating spline based linear

This paper investigates the anti-windup design for networked time-delay systems subject to saturating actuators under the round-robin protocol. Firstly, the actual measurement output is represented by the model that is dependent on a periodic function. Then, using the generalized delay-dependent sector condition, the augmented periodic Lyapunov-Krasovskii functional together with certain inequalities

We study the spectral properties of flipped Toeplitz matrices of the form Hn(f)=YnTn(f), where Tn(f) is the n×n Toeplitz matrix generated by the function f and Yn is the n×n exchange (or flip) matrix having 1 on the main anti-diagonal and 0 elsewhere. In particular, under suitable assumptions on f, we establish an alternating sign relationship between the eigenvalues of Hn(f), the eigenvalues of Tn(f)

Deep learning still has drawbacks regarding trustworthiness, which describes a comprehensible, fair, safe, and reliable method. To mitigate the potential risk of AI, clear obligations associated with trustworthiness have been proposed via regulatory guidelines, e.g., in the European AI Act. Therefore, a central question is to what extent trustworthy deep learning can be realized. Establishing the described

This study explores a distinctive scenario within the e-commerce platform supply chain. To assess the performance of these entities, we develop models for both centralized and decentralized decision-making frameworks. Furthermore, we investigate the stability and dynamic behavior of the system during prolonged decentralized model interactions. We found that centralized decision-making has a significant

This paper presents a two-grid finite element method for solving semilinear fractional evolution equations on bounded convex domains. In contrast to existing studies that assume strong regularity for the exact solution, our approach rigorously addresses the limited smoothing properties of the fractional model. Through a combination of semigroup theory and energy estimates, we derive optimal error bounds

The exponential stabilization for spatial multiple-fractional advection-diffusion-reaction system (SMFADRS) is considered, and for the disturbed SMFADRS, the finite-time H∞ stabilization is investigated. To ensure the considered system to achieve the desired performance, a distributed controller is designed to be located in the sub-intervals of the whole spatial domain. Then, by deriving an improved

We consider the steady 2D and 3D Navier-Stokes equations with homogeneous mixed boundary conditions and the action of an external force. The classical do-nothing (CDN) boundary condition is replaced by a regularized directional do-nothing (RDDN) condition which depends on a parameter 0<δ≪1. After establishing the well-posedness of the Navier-Stokes equations with RDDN condition, we prove the convergence

We study a general class of bivariate fractional integral operators, derived from bivariate analytic kernel functions by a double substitution of variables and a double convolution. We also study the associated bivariate fractional derivative operators, derived by combining partial derivatives with the aforementioned fractional integrals. These operators give rise to a theory of two-dimensional fractional

This paper deals with numerical computation and analysis for the initial value problems (IVPs) of linear nonhomogeneous neutral pantograph equations. For solving this kind of IVPs, a class of extended k-step variable-coefficient backward differentiation formula (BDF) methods with fully-geometric grid are constructed. It is proved under the suitable conditions that an extended k-step variable-coefficient

Weighted compact nonlinear schemes are a class of high-order finite difference schemes that are widely used in applications. The schemes are flexible in the choice of numerical fluxes. When applied to complex configurations, curvilinear grids are often applied, where the symmetric conservative metric method can be used to ensure geometric conservation laws. However, for complex configurations it may

This paper investigates the problem of finite-time H∞ fault-tolerant control for uncertain Markov jump systems with generally bounded transition probabilities using a two-step dynamic event-triggered approach. A novel framework is proposed to optimize data transmission and improve fault tolerance via this approach. First, a dynamic event-triggered mechanism and an observer are introduced where a virtual

In this paper we propose a novel macroscopic (fluid dynamics) model for describing pedestrian flow in low and high density regimes. The model is characterized by the fact that the maximal density reachable by the crowd – usually a fixed model parameter – is instead a state variable. To do that, the model couples a conservation law, devised as usual for tracking the evolution of the crowd density, with

We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense. Namely, we prove a Sharkovskii-type theorem: if the system has a periodic orbit of basic period m, then it must have all periodic orbits of periods n⊳m, for n preceding

Combining the stabilized scalar auxiliary variable approach and the variable-step second-order backward difference formula, an adaptive time-stepping scheme is proposed for the two-mode phase-field crystal model with face-centered-cubic ordering. Specifically, introduce an auxiliary variable to handle the nonlinear term and obtain a new equivalent system, then perform a variable-step second-order approximation

Presume the uniform smooth Banach space E to possess p-uniform convexity for p≥2. In E, the VIP stands for a variational inequality problem and the CFPP a common fixed point problem of Bregman’s relative asymptotic nonexpansivity operator and finite Bregman’s relative demicontractions. We design and deliberate two adaptive double-inertial Bregman’s projection schemes with linesearch procedure for tackling

The lattice Boltzmann method (LBM) for compressible flow is characterized by good numerical stability and low dissipation, while the conventional finite volume solvers have intrinsic conversation and flexibility in using unstructured meshes for complex geometries. This paper proposes a strategy to combine the advantages of the two kinds of solvers by designing a finite volume solver to mimic the LBM

For an arbitrary given span of high dimensional multivariate Chebyshev polynomials, an approach to construct spatial discretizations is presented, i.e., the construction of a sampling set that allows for the unique reconstruction of each polynomial of this span.

In this paper, we study direct and inverse problems for Dirac systems with complex-valued potentials on p-star-shaped graphs. More precisely, we firstly obtain sharp 2-term asymptotics of the corresponding eigenvalues. We then formulate and address a Horváth-type theorem, specifically, if the potentials on p−1 edges of the p-star-shaped graph are predetermined, we demonstrate that the remaining potential

Accumulation operators play an important role in grey system models. However, with specific mechanism, each operator is effective only for specific temporal characteristics of the time series. In order to further utilize the effectiveness of existing accumulation operators, especially the ones with nonlinear features such as fractional order accumulation and information priority accumulation, this

In this work, we consider an inverse source problem for the time-space fractional diffusion equation with homogeneous Dirichlet boundary conditions, in which the spatial operator under consideration is the fractional Sturm–Liouville operator. We demonstrate that this inverse source problem is ill-posed in the sense of Hadamard and exhibit the uniqueness and conditional stability of its solution. To

In this paper, a third-order time adaptive algorithm with less computation, low complexity is provided for shale reservoir model based on coupled fluid flow with porous media flow. This algorithm combines a method of three-step linear time filters for simple post-processing and a second-order backward differential formula (BDF2), is third-order accurate in time, and provides no extra computational

We consider a two-dimensional sharp-interface model for solid-state dewetting of thin films with anisotropic surface energies on curved substrates, where the film/vapor interface and the substrate surface are represented by an evolving curve and a static curve, respectively. The continuum model is governed by the anisotropic surface diffusion for the evolving curve, with appropriate boundary conditions

In this work, we propose and analyze a stochastic SIQRS epidemic model with the disease transmission rate driven by a log-normal Ornstein–Uhlenbeck process. By establishing a series of Lyapunov functions, we derive sufficient criteria for the asymptotical stability of the positive equilibrium of the system which suggests the prevalence of the disease in the long term. This work provides a basis for

We consider the absolute value equation (AVE) Ax−|x|=b, where the diagonal entries of A∈Rn×n are all greater than 1 and 〈A〉−I is an irreducible singular M-matrix (〈A〉 is the comparison matrix of A). We investigate the existence and uniqueness of solutions for the AVE. The AVE does not necessarily have a unique solution for every b∈Rn, so most of the existing convergence results for various iterative

The paper investigates a pivotal condition for the Bobkov-Tanaka type spectrum for double-phase operators. This condition is satisfied if either the weight w driving the double-phase operator is strictly positive in the whole domain or the domain is convex and fulfils a suitable symmetry condition.

This study refines the two-stage social insect model of Kang et al. (2015) by incorporating a nonlinear egg cannibalism rate. The introduction of nonlinearity presents analytical challenges, addressed through the application of the compound matrix method to rigorously establish global stability. The analysis reveals complex dynamical behaviors, including two distinct types of bistability: one between

Individual interactions play a crucial role in the co-evolution process of awareness and epidemics; these interactions involve pairwise and higher-order types. Previous research usually assumed that individual interactions are all valid and static, overlooking the fact that some interactions may be invalid and time-varying. Notably, diffusion phenomena cannot occur if interactions lose their validity

We consider a nonlinear eigenvalue problem driven by the nonautonomous (p,q)-Laplacian with unbalanced growth. Using suitable Rayleigh quotients and variational tools, we show that the problem has a continuous spectrum which is an upper half line and we also show a nonexistence result for a lower half line.

We consider the coupled system of the Landau–Lifshitz–Gilbert equation and the conservation of linear momentum law to describe magnetic processes in ferromagnetic materials including magnetoelastic effects in the small-strain regime. For this nonlinear system of time-dependent partial differential equations, we present a decoupled integrator based on first-order finite elements in space and an implicit

In this research article, we have simulated the solutions of three types of (classical) moving boundary models in ductal carcinoma in situ by an efficient temporal-spatial spectral collocation method. In all of these three classical models, the associated fixed (spatial) boundary equations are localized by the numerical scheme. In the numerical scheme, Laguerre polynomials and Hermite polynomials are

A proper conflict-free l-coloring of a graph G is a proper l-coloring satisfying that for any non-isolated vertex v∈V(G), there exists a color appearing exactly once in NG(v). The proper conflict-free chromatic number, denoted by χpcf(G), is the minimal integer l so that G admits a proper conflict-free l-coloring. This notion was proposed by Fabrici et al. in 2022. They focus mainly on proper conflict-free

To investigate the impact of the expanding region and harvesting pulses on population dynamics, we propose a one-dimensional logistic model that integrates harvesting pulses on a growing domain. By employing the eigenvalue method, we derive the explicit expression of the ecological reproduction index ℜ0 and analyze its pertinent properties. Subsequently, we explore the asymptotic behavior of solutions

In this paper, we analyze the unconditionally optimal error estimates of the linearized virtual element schemes for a class of nonlinear wave equations. For the general nonlinear term with non-global Lipschitz continuity, we consider a modified Crank–Nicolson scheme for the time discretization and a conforming virtual element method for the spatial discretization. Using the mathematical induction and

An accurate constitutive model for viscoelastic plates with variable thickness is crucial for understanding their deformation behaviour and optimizing the design of material-based devices. In this study, a variable order fractional model with a precise order function is proposed to effectively characterize the viscoelastic behaviour of variable thickness plates. The shifted Legendre polynomials algorithm

In this study, we introduce a phase field model designed to represent the intricate physical dynamics inherent in selective laser melting processes. Our approach employs a phase-field model to simulate the liquid–solid phase transitions, fluid flow, and thermal conductivity with precision. This model is founded on the variational principle, aiming to minimize the free energy functional, thereby guaranteeing